Basically live and die by Gmail - very rarely goes down; works across all my devices; always in sync and always up to date. The spam filter is pretty damn good too.
And as much as I'm a pretty die hard Apple user - I really love Microsoft Outlook for iOS - instant notification of new emails.
Any web developer needs to test emails with other providers so the random AOL, Yahoo, Microsoft Live, etc... accounts are maintained also.
For sending out email notifications and newsletters and such - I'm a big fan of AWS SES but due to complexity, tend to go with Mailgun often for projects that require it (old habits die hard).
I've liked Mailgun due to the API being easy to use - but they've been really flaky lately (as I've mentioned elsewhere) - and I'm considering a coup to AWS SES for all projects. It'll require a lot more code to do what's fairly easy in Mailgun - but once some basic structures are setup - copy / paste / modify to other projects.
What I want - and if I had the time to build it myself, I would - is a system where I can setup email templates - say, 1 for new user registration, 1 for stripe invoice, 1 for whatever. Those templates would use handlebars (of sorts) where I can pass in a json array and fill it in - example: Hello {{user.fullname}} - each template would have a unique ID of course.
Then I could send an API request to this service with the basics - to, from, subject, template_id and pass in my array of values and have it send the email off automatically or schedule it.
Consistent emails, every time.
(I've yet to find something like this)
Mario Giambanco
Director of User Experience Development